Overview of the COMPASS results on the nucleon spin

Celso Franco (LIP – Lisboa) on behalf of the COMPASS collaboration

PT ~ 50% / 90%

COMPASS target: 6LiD (2002-06) - NH3 (2007-11)

T ~ 50 mK (3He / 4He)

180 mrad

200 GeV

Unpolarised Helicity Transversity Transverse Momentum Generalized Parton

Motivation

● Motivation I: Nucleon spin structure

(2SzN

h )= 12Δ Σ + Lz , JM

q + ΔG + Lz , JMg

Where does the proton spin (complex structure in QCD) come from?

q(x), g(x) ∆q(x), ∆g(x) ∆Tq(x) (k

T) Dependent PDFs Distributions

Jaffe-Manohar sum rule

Q2 = -q2

= E – E'x = Q2 / 2My = / E

GPDs

Mostly studied in polarised Deep Inelastic Scattering

(DIS)

=12Δ Σ + Lz ,Ji

q + J Jig =

12( lim ∫

−1

+1dx x [H (x ,ξ , t)+E (x , ξ , t )])+J Ji

g

Ji sum rulet→0

= ∫01 u x u x d x d x

s x s x dx

Lq related to TMDs Lq related to GPDs

G = ∫01 g x dx

●

●

●

●

● Motivation II: Parton Distribution Functions (PDFs), TMDs and GPDs

Description of the nucleon structure at leading twist(when the intrinsic transverse momentum of quarks, k

T , is also taken into account)

UnpolarisedLongitudinal Polarisation

Transverse Polarisation

Unpolarised

Longitudinal Polarisation

Transverse Polarisation f

1T

⊥(Sivers)

g1

(Helicity)

f1

(Number density)

⊥h1

(Boer Mulders)

Quark

Nucleon

(Worm Gear)

g1T

(Worm Gear)

h1L⊥

h1

h1T⊥

Surviving kT

integration

Contains information about the Orbital Angular Momentum

(OAM) of quarks

(Transversity)

(Pretzelosity)

Study ∆q(x, Q2) and ∆g(x, Q2)

Study q(x, Q2)and g(x, Q2)

Study ∆Tq(x, Q2)

8 TMD PDFs are required:

ΦCollTw− 2 x =

12 {q xS L5 q x }

{ ST 5 1T q x}Investigated at COMPASS via

measurement of spin asymmetries

{ S L5 1T q x}

COMPASS results with a longitudinally polarised target

COMPASS results on g1: A1(x ,Q2

) =σ γ*N−σ γ* N

σ γ* N

≈∑q

eq2Δq (x ,Q2

)

∑qeq

2 q (x ,Q2)=

g1(x ,Q2)

f1(x , Q2)

→→

Deuteron Proton

Polarised PDFs from the NLO-QCD fits to the g1

d and g1

p data

● Small sensitivity to light sea and gluon helicities

● Quark helicity: ∆Σ = ∫∆qs(x)dx ϵ [0.256, 0.335]

● Gluon helicity: ∆G = ∫∆g(x)dx → Not well constrained

QCD fits – Idea:

Initial parametrisation in x at fixed Q2:

Minimisation procedure:

( )

Three scenarios, ∆G < 0, ∆G ~ 0 and ∆G > 0, cover all possible results on the polarised PDFs (the largest uncertainty arises from the choice of the functional forms):

∆Σ = +0.30 ± 0.01 ± 0.02 ∆s = −0.08 ± 0.01 ± 0.02

PLB 647(2007) 8-17 (only g1

d):

Extraction of the quark helicity distributions from Semi-Inclusive DIS (SIDIS)

A1, p /dh

x ,z ,Q2 ≈

∑qeq

2 q x , Q2Dqhz , Q2

∑qeq

2 qx , Q2Dq

hz , Q2

tags the quark flavour

● We have at Leading Order (LO) in QCD :

– Unpolarised PDFs ( q(x, Q2) ) → MRST04

– Fragmentation function of a quark to a hadron ( D

q

h(z, Q2) ) → DSS parameterisation

● Results for A1, (p/d)

( allows the separate extraction of ∆u, ∆d, ∆u, ∆d, ∆s and ∆s ):h

Quark helicities from SIDIS: Q2 = 3 (GeV/c)2 and x < 0.3

sSIDIS = −0.01 ± 0.01stat. ± 0.01syst. @ 0.003 x 0.3

• COMPASS PLB693(2010)227, ○ HERMES, DSSV

°

COMPASS PLB 693 (2010) 227

No flavour asymmetry in the polarised sea

● Sea distributions ~ 0

● Flavour separation until x ~ 0.004

Assume ∆s = ∆s

Direct measurement of the gluon polarisation (∆g/g) at LO in QCD

Two methods to tag this process are used:

● Open Charm production

● High-pT hadron pairs

photon-gluon fusion process (PGF)

ANPGF

=∫d s PGF g xg , s

∫d s PGFg xg , s

≈ ⟨aL LPGF ⟩ g

g

Obtained from Monte Carlo and parameterised by a Neural Network (to be used on data)

– Hard scale: Mc

2

– No intrinsic charm in COMPASS kinematics

– No physical background

– Weakly model dependent– Low statistics

– High statistics

– Hard scale: Q2 or ΣpT

[Q2 > 1 or Q2 < 1 (GeV/c)2 ]

– Model dependent

– Physical background

– γ*g → cc ⇒ reconstruct D0 mesons

– γ*g → qq ⇒ reconstruct 2 jets or h+h−

2

Results on the gluon polarisation

1st world measurement at NLO

World data at LO

Phys. Rev. D(2013) 052018

New results from the all-pT analysis

∆g/g = -0.13 ± 0.15 ± 0.15@ ⟨ x

g ⟩ = 0.20

Phys. Lett. B 718 (2013) 922

Spin asymmetries at Q2 < 1 GeV2 / c2 (AL L =σμN − σμN

σμN)

for an indirect extraction of ∆G

→→

Comparison with calculations (V. Vogelsang, M. Stratmann and B. Jager) of ALL

at NLO:..

COMPASS results with a transversely polarised target

Interpretation of Collins & Sivers asymmetries in terms of TMDs

measured by fitting the corresponding (φh, φ

S) distributions (from σSIDIS) in different x, z, p

T

h bins

Collins Angle Sivers Angle

SivA

Depends on spin!Studies from SIDIS

Results on the Collins asymmetry (correlation between the hadron pT &

PLB 692 (2010) 240, PLB 717 (2012) 376 NPB 765 (2007) 31

h1

u -h1

d

the quark transverse spin in a transversely polarised nucleon), h1

d and h1

u

PROTONDEUTERON

h1

⊥fav -h1

⊥unf

Good agreement with A12

and A0

Fits to theBelle data

for the u quark

Results on the Sivers asymmetry (correlation between the nucleon transverse spin and the quark/gluon k

T) for quarks and gluons

A. Bacchetta and M. Radici● A clear ASiv

(quarks) signal is seen for h+ proton

● New result on the gluon Sivers asymmetry:

data (f1T

u -f1T

d on deuteron):

J q = (1 /2)Δ Σ + Lq

q=∫0

1dx x [H q

(x ,0 ,0)+Eq(x ,0 ,0)]

q(x)

PLB 692 (2010) 240, PLB 717 (2012) 383

APGF

(deuteron) = - 0.14 ± 0.15 @<xG> = 0.13

Possibility to access the

OAM

Few examples of future measurements at COMPASS

COMPASS future I (2014-2015): TMDs from polarised Drell-Yan (DY)

uud

d uγ∗

µ+

µ−

X

P

π − ● Convolution of 2 TMDs (no FF involved):

● Test of the TMD universality factoriza- tion approach (for the description of SSA):

DY ∝ fu / − f ' u / P

Main modifications in the spectrometer

● The production mechanism and the polarisation of J/Ψ will also be studied

f 1T∣ = − f 1T

∣ h1

∣ = −h1

∣

DY DIS DY DIS&

Large acceptance in the valence region where large single spin asymmetries (SSA) are expected

DRELL-YAN PROCESS

NH3

Polarised target Absorber muon pairs Dipolemagnet

Clean access to 4 azimuthal modulations

(Boer-Mulders, Sivers, Pretzelosity and Transversity)

COMPASS future II (2016-2017): GPDs and nucleon tomography

● The GPD H will be determined by studying the azimuthal dependence of the DVCS

● For the cases of ξ = 0, we have a

Deeply Virtual Compton Scattering (DVCS)

purely transverse ∆⊥

2:Tomography!

● Measurement of 4 generalised parton distributions (GPDs) for quarks: H, E, H, E(x, ξ , t)

– Contains normal PDF and elastic form factor as limiting cases: q(x) = H(x,0,0) and F(t) = ∫ dx H(x, ξ , t)

– Correlates transverse spatial and longitudinal momentum degrees of freedom (nucleon tomography)

– Access the OAM of quarks via the Ji sum rule

~ ~

cross-section (combining the data of µ+ and µ− beams on a liquid hydrogen target):

Summary

● Gluon contribution to the nucleon spin:

● All measurements point to zero or small contribution

● Quark contribution to the nucleon spin:

● Extraction for all flavours from SIDIS (more knowledge on FF is needed for ∆s)

● A global contribution of 30% was measured with high precision

● Transversity and TMDs

● Precise results on collins and Sivers asymmetries

● Exciting future program in preparation:

3D imaging of the nucleon Unpolarised SIDIS measurements

TMDs (DY) GPDs (DVCS)

● Contribution of the gluon helicity to the nucleon spin:

– All direct measurements point to zero or small contribution

– ∆G is not well constrained by the NLO-QCD fits to the g1 data

– Present calculations of ALL

do not agree simultaneously with proton and deuteron data

● Contribution of the quark helicity to the nucleon spin:

– Extraction for all flavours from SIDIS (also from the NLO-QCD fits to the g1 data)

– A global contribution of 30% was measured with good precision

● Transversity and TMDs

– Precise measurements of the Collins and Sivers asymmetries

– New result on the gluon Sivers asymmetry (compatible with zero)

● Hadron multiplicities to improve the knowledge on: D

q

h(z), s(x) and ∆s(x)

● Boer-Mulders TMD: h1

(x, kT)